In this dissertation, we use theory and computation to conduct three projects in the area of nano-optics. In the first project, we study optical coherence conversion using a plasmonic hole array. This work led to the discovery of the optical coherence band gap. In the second project, we develop a method of producing sub-wavelength arrangements of optical vortices. We demonstrate the validity of this method and propose an experimental realization. In the third project, we apply the techniques of the second to design superresolution lenses.
